高等数学求二重积分∫[0,1]dx∫[x,1]e^
求二重积分∫[0,1]dx∫[x,1]e^-y²dy=?
关键是交换积分次序， ∫[0,1]dx∫[x,1]e^(-y²)dy =∫∫《D>e^(-y²)dxdy =∫[0,1]dy∫[0,y]e^(-y²dx =∫[0,1,y*e^(-y²)]dy =(-1/2)e^(-y²)|<0,1> =(1/2)(1-1/e)。